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This work examines the question of how a Hubbard U correction to a local exchange–correlation functional compares with adding Hartree–Fock exchange to a local functional for both solid-state and molecular properties. We compute a solid-state property, namely the band gap, and thermochemical molecular properties, in particular, main-group bond energies, transition metal–ligand bond energies, and barrier heights, to elucidate whether the DFT+U method mimics hybrid DFT. We find that a calculation with a Hubbard U correction may or may not mimic a hybrid functional—depending on the atom, the subshell, and the property to which it is applied. For band gaps, we find that adding a Hubbard U correction to the valence d orbitals of transition metals increases the band gap, which thereby gets closer to the experimental value, while adding a Hubbard U correction to valence s or p orbitals of main-group elements need not always increase the band gap. For molecular thermochemistry, we find that adding a Hubbard U correction to a local density functional need not have the same effect as adding Hartree–Fock exchange to a local density functional. For example when compared to a DFT calculation with a local exchange-correlation functional, hybrid DFT increases the barrier height in all cases, but DFT+U does not always increase the barrier height. For the band gaps of transition metal monoxides, the Hubbard-corrected results lowered the mean errors significantly and were comparable to what could be achieved with a much more expensive hybrid functional, but for reaction barrier heights and bond energies of molecules, the Hubbard correction was found to lower the mean error by only approximately a kcal/mol. As part of the analysis, we also compare VASP and Gaussian 09 calculations for the same density functional. [ABSTRACT FROM AUTHOR]

Hybrid density functional theory, which is a combined Hartree-Fock and density functional method, provides a simple but effective way to incorporate nonlocal exchange effects and static and dynamical correlation energy into an orbital-based theory with affordable computational cost for many important problems of gas-phase chemistry. The inclusion of a reaction field representing an implicit solvent in a self-consistent hybrid density functional calculation provides an effective and efficient way to extend this approach to problems of liquid-phase chemistry. In previous work, we have parameterized several models based on this approach, and in the present article, we present several new parameterizations based on implicit solvation models SM5.43 and SM5.43R. In particular, we extend the applicability of these solvation models to several combinations of the MPWXhybrid-density functional with various one-electron basis sets, where MPWXdenotes a combination of Barone and Adamo’s modified version of Perdew and Wang’s exchange functional, Perdew and Wang’s correlation functional, and a percentageXof exact Hartree-Fock exchange. SM5.43R parameter optimizations are presented for the MPWX/MIDI!, MPWX/MIDI!6D, and MPWX/6-31+G(d,p) combinations withX=0 (i.e., pure density functional theory), 25, 42.8, and 60.6, and for MPWX/6-31G(d) and MPWX/6-31+G(d), withX=0, 42.8, and 60.6; this constitutes a total of 18 new parameter sets. [Note that parameter optimizations using MPW25/6-31G(d) and MPW25/6-31+G(d) were carried out in a previous SM5.43R parameterization.] For each of the five basis sets, we found no significant loss in the accuracy of the model when parameters averaged over the four values ofXare used instead of the parameters optimized for a specific value ofX. Therefore for each of the five basis sets used here, the SM5.43R and SM5.43 models are defined to have a single parameter set that can be used for any value ofXbetween 0 and 60.6. The new models yield accurate free energies of solvation for a broad range of solutes in both water and organic solvents. On the average, the mean-unsigned errors, as compared with those from experiment, of the free energies of solvation of neutral solutes range from 0.50 to 0.55 kcal/mol and those for ions range from 4.5 to 4.9 kcal/mol. Since the SM5.43R model computes the free energy of solvation as a sum of bulk-electrostatic and non-bulk-electrostatic contributions, it may be used for detailed analysis of the physical effects underlying a calculation of the free energy of solvation. Several calculations illustrating the partitioning of these contributions for a variety of solutes inn-hexadecane, 1-octanol, and water are presented. [ABSTRACT FROM AUTHOR]

Beginning with the MIDI! basis set (also called MIDIX), we introduce the MIDIX+, MIDIY, and MIDIY+ basis sets. Using correlated ab initio and hybrid density functional theory, we compare their performance to that of several existing basis sets for electronic structure calculations. The new basis sets are tested with databases of 358 energies of reactions, 44 barrier heights, 31 electron affinities, 18 geometries, and 29 dipole moments. The MIDI!, MIDIX+, MIDIY, and MIDIY+ basis sets are shown to be cost-efficient methods for calculating relative energies, geometries, and dipole moments. The MIDIX+ basis is shown to be particularly efficient for calculating electron affinities of large molecules. [ABSTRACT FROM AUTHOR]